

A213411


G.f. A(x) = 1 / (1  x^a(0) / (1  x^a(1) / (1  x^a(2) / ... ))).


3



1, 1, 2, 4, 9, 20, 45, 101, 228, 514, 1160, 2617, 5906, 13327, 30075, 67868, 153156, 345621, 779953, 1760094, 3971951, 8963378, 20227382, 45646511, 103009086, 232457449, 524579615, 1183802763, 2671451479, 6028582814, 13604518396, 30700900429, 69281782713
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OFFSET

0,3


LINKS

Table of n, a(n) for n=0..32.


EXAMPLE

1 + x + 2*x^2 + 4*x^3 + 9*x^4 + 20*x^5 + 45*x^6 + 101*x^7 + 228*x^8 + ...


MATHEMATICA

terms = 29; f[k_] := If[k >= 0, x^a[k], 1]; F[m_] := ContinuedFractionK[ f[k], 1, {k, 1, m}]; s[0] = {a[0] > 1}; eq[n_] := eq[n] = Normal[( F[n1] /. s[n1]) + O[x]^(n+1)]  Sum[a[k] x^k, {k, 0, n}] == 0 /. s[n1]; s[n_] := s[n] = Join[s[n1], SolveAlways[eq[n], x] [[1]]]; Reap[ Do[ Print["a(", n, ") = ", an = a[n] /. s[n]]; Sow[an], {n, 0, terms1} ]][[2, 1]] (* JeanFrançois Alcover, Jul 16 2017 *)


CROSSREFS

Sequence in context: A085584 A080019 A052534 * A080135 A227978 A206741
Adjacent sequences: A213408 A213409 A213410 * A213412 A213413 A213414


KEYWORD

nonn,nice


AUTHOR

Michael Somos, Jun 10 2012


STATUS

approved



